640 

IL61b 

v.14:47 


LIBRARY  OF  THE 

UNIVERSITY  OF  ILLINOIS 

AT  URBANA-CHAMPAIGN 


University  of 

Illinois  Library 

atUrbana-Champaigr 

ACES 


'640 
"IL61b 
v. 14:47  University  of  Illinois 

A  Library  at 

Urbana-Champaign 

ACES 
FATS  AND  OILS  IN  uuuKhK\ 

SOUR(  ES  AND  CLASSES 

Fats  are  derived  from  both  the  animal  and  the  vegetable  king- 
doms. A  few  decades  ago,  the  former  source  was  the  chief  one  used 
by  the  people  of  this  country,  but  of  late  years  the  Latter  has  been 
drawn  upon  more  extensively.  The  chief  animal  fats  used  as  food  are 
cream,  butter,  lard,  and  suet.  The  common  vegetable  Eats  are  olive, 
corn,  Kind  nut  oils;  there  arc  on  the  market,  also,  com- 
pounds of  animal  and  vegetable  fats  and  some  products,  such  as 
('risen,  made  by  treating  an  oil  with  hydrogen.  In  the  home,  other 
fats,  such  as  beef  and  bacOn  drippings  and  chicken  fat,  are  obtained 
by  the  cooking  of  meats.  These,  if  carefully  saved  and  judiciously 
ased,  will  Lower  considerably  the  cost  of  fat  in  the  household. 

As  in  other  food  supplies,  the  accessibility  determines  the  amount 
of  any  kind  to  be  used,  and  the  fact  will  always  remain  that  the  avail- 
able and  the  cheapest  foods  are  the  ones  which  will  be  employed.  It 
would  be  foolish  to  counsel  the  woman  with  plenty  of  fresh  cream  and 
butter  at  her  immediate  command  to  purchase  olive  oil  at  one  dollar 
per  quart.  It  is  equally  foolish  to  recommend  cream  at  fifty  cents  per 
quart  to  the  undernourished  factory  girl.  Each  consumer  must  study 
the  possibilities  and  limitations  of  her  own  source  of  supply,  and  must 
act  accordingly. 

CHEMICAL    AND    PHYSICAL   PROPERTIES 

All  t'ats  and  oils  are  composed  of  the  elements  carbon,  hydrogen, 
and  oxygen.  These  elements  are  combined  in  such  a  way  as  to  form 
compounds  of  glycerin  and  fatty  acids  called  glycerids.  That  is  in 
say,  all  fats  and  oils  contain  glycerin,  but  the  fatty  acid  may  differ. 
and  upon  the  acid  depends  the  melting  point  and  other  distinguishing 
characteristics  of  the  compound.  The  compound  is  called  a  fat  if  its 
melting  point  is  so  high  as  to  make  it  solid  at  ordinary  temperature, 
and  an  oil  if  its  melting  poinl  is  so  low  ,-is  to  make  it  Liquid  at  ordinary 
room  temperature.  The  three  most  important  fatly  acids  are  palmitic. 
aric,  and  oleic.  The  first  two  are  much  alike,  both  the-  acids  and 
the  fats  in  which  they  predominate  being  hard  substances  of  high  melt- 
ing point,  said  chemically  to  be  saturated.     Vegetable  fats  and  oils 


4  University  of  Illinois  Bulletin  [July, 

contain  more  palmitic  than  stearic  acid,  while  the  contrary  is  true  of 
fats  and  oils  of  animal  origin.  Oleic  acid  and  the  oils  in  which  it 
predominates  are  quite  different.  Their  melting  point  is  low  and  they 
are  chemically  unsaturated.  The  hard  tallow  of  beef  and  mutton  con- 
tains glycerin  combined  with  large  amounts  of  stearic  acid,  some 
palmitic,  and  relatively  little  oleic.  Lard  contains  a  larger  proportion 
of  oleic  acid  compounds.  Olive  oil  is  almost  entirely  a  glycerid  of 
oleic  acid. 

It  has  been  found  possible  to  change  some  oils  into  solid  fats  and 
to  harden  fats  which  were  already  solid  by  heating  the  oil  under 
pressure  with  hydrogen,  in  the  presence  of  a  catalyst,  such  as  nickel. 
The  unsaturated  fats,  which  are  soft,  take  up  hydrogen  to  form  sat- 
urated, fats,  which  are  less  soft.  These  hydrogenized  fats  are  coming 
to  be  more  and  more  commonly  used,  and  new  forms  under  varied 
names  are  appearing  constantly  on  the  market. 

In  the  presence  of  moisture,  fats  become  rancid  on  exposure  to 
air,  or  warmth  and  light.  Thfs  rancidity  is  developed  by  a  process  of 
oxidation  and  hydrolysis,  and  generally  develops  more  readily  in  oils 
than  in  solid  fats. 

Fats  have  different  melting  points,  ranging  from  the  oils  which 
are  liquid  at  ordinary  temperatures  and  solidify  below  0°  C.  to  mutton 
fat,  one  of  the  hardest,  having  a  melting  point  of  49°-50°  C.  High 
heat  causes  smoking.  This  is  due  to  decomposition,  altho  some  decom- 
position may  occur  at  a  lower  temperature.  A  list  of  fats,  with 
their  smoking  temperatures,  is  given  below.  The  tests  were  made  on 
one  cup  of  fat  in  a  small  saucepan,  six  inches  in  diameter. 

Table  1. — Smoking  Temperatures  of  Fats 


Kind  of  fat 

Smoking  temperature 

Cottonseed  oil  (Wesson) 

degrees  Centigrade 
225 
223 
217 

Suet 

210 
208 
175 
156 
145 
117 

Katherine  Blunt  and  Clara  Feeney1  found  the  smoking  tempera-  4 
ture  of  a  fat  to  vary  according  to  the  amount  of  surface  exposed,  the 


Mournal  of  Home  Economics,  Vol.  VII,  No.  10,  p.  535. 


1917] 


#£6S 


Fats  and  Oils  in  Cooking 


amount  of  free  acid,  and  the  amount  of  foreign  material  present,  such 
as  particles  of  food  or  crumbs.  The  above  smoking  temperatures  will, 
then,  vary  according  to  the  size  and  shape  of  the  utensil  used,  being 
lower  for  a  wider  pan  and  higher  for  a  more  narrow  one,  as  in  the 
former  case  the  surface  exposure  is  greater.  They  would  also  be  low- 
ered by  rancidity  or  repeated  use  of  the  fat,  which  means  increased 
free  acid,  or  by  the  presence  of  foreign  particles.  However,  under 
similar  conditions,  the  relation  of  the  temperatures  should  remain  un- 
changed. 

Some  results  of  the  work  done  by  Blunt  and  Feeney  follow. 


Kind  of  fat 


Cottonseed  oil  (Wesson) . .  . 

Snowdrift 

Crisco 

Leaf  lard 

Butter  fat 

Leaf  lard  (heated  5  hours) . 

Bulk  lard , 

A  much  used  lard 

Olive  oil 


Smoking    temperature 
in  evaporating  dish 


degrees  Centigrade 
233 
232 
231 
221* 
208* 
207 
194 
190 
175 


Free  acid,  as  oleic 


percent 
0.07 
0.06 
0.13 
0.15 
0.28 
0.34 
0.51 
0.61 
0.92 


It  may  be  seen  readily  that,  while  the  temperatures  in  the  two 
tables  are  not  the  same,  nevertheless  relatively  they  fall  in  the  same 
order.  The  differences  are  to  be  explained  by  the  fact  that  a  larger 
and  wider  utensil  was  used  in  the  first  case  than  in  the  second ;  conse- 
quently, smoking  began  at  a  lower  temperature.  This  range  in  smok- 
ing temperatures  shows  that  the  old  time  test  of  fat  for  frying,  "smok- 
ing hot, ' '  does  not  give  the  same  temperature  for  all  fats ;  hence,  other 
tests  must  be  relied  upon.  The  characteristics  of  a  good  fat  for  a  fry- 
ing medium  are:  first,  a  high  smoking  temperature;  second,  the  smoke 
should  increase  slowly;  and,  third,  the  smoke  should  not  be  irritating 
in  character.  The  first  smoke  from  olive  oil,  for  example,  is  not  irri- 
tating and  it  increases  very  gradually,  so  that  at  300°C.  it  is  by  no 
means  as  disagreeable  as  is  lard  which  starts  to  smoke  at  a  higher  tem- 
perature. The  objections  to  fats  which  smoke  readily  are  the  irrit;  t- 
[ng  odor  and  the  impaired  quality  of  the  fat  for  further  frying. 
Smoking  is  an  indication  of  decomposition,  and  the  fat  which  decom- 
poses most  on  heating  can  be  used  the  fewest  number  of  times.  From 
this  last  standpoint,  the  cottonseed  products  are  especially  desirable 
as  a  medium  for  frying. 


6  University  of  Illinois  Bulletin*  [July, 

VALUE  AS  FOOD 

Fats  and  oils  are  of  value  in  the  diet  chiefly  because  for  a  given 
weight  they  yield  more  energy  than  do  any  of  the  other  foodstuffs. 
One  gram  of  carbohydrate  or  of  protein  yields  four  calories  of  energy 
in  the  form  of  heat,  but  one  gram  of  fat  yields  nine  calories.  For  this 
reason,  fats  are  of  especial  value  to  the  manual  laborer,  to  the  person 
who  works  out-of-doors  in  cold  weather,  and  to  the  thin  or  anemic 
person  who  has  no  reserve  of  fat  in  his  own  body.  Some  of  the  fats 
and  oils,  because  of  their  greater  degree  of  absorption  from  the 
digestive  tract,  are  of  greater  value  in  giving  energy  than  are  others. 
Fats  having  low  melting  points  have  been  found  to  be  more  completely 
assimilated  than  those  having  high  melting  points.1  Therefore,  olive 
or  Wesson  Oil  and  butter,  which  have  low  melting  points,  are  to  be 
chosen  as  foods  that  will  be  Ave'll  absorbed,  and  hence  the  ones  from 
which  the  greatest  fuel  value  will  be  obtained.  Another  factor  which 
influences  the  digestion  of  a  fat  is  the  degree  of  its  emulsification.  Only 
emulsified  fats  are  digested  to  any  appreciable  extent  in  the  stomach, 
and  the  finer  the  emulsification  the  greater  is  the  rapidity  of  digestion 
and  absorption  in  the  duodenum  and,  often,  the  greater  is  the  complete- 
ness of  utilization.  Fats  of  milk  and  of  egg  are  examples  of  this  fine 
emulsification. 

Some  people  cannot  digest  large  amounts  of  fat.  This  foodstuff 
delays  the  emptying  of  the  stomach,  retards  the  secretion  of  the  hydro- 
chloric acid,  and  also  promotes  regurgitation  thru  the  pylorus  into 
the  stomach,  thus  neutralizing  the  acid  that  is  present  there.  All  of 
these  may  occur  when  foods  are  fried  or  sauted  so  as  to  absorb  large 
amounts  of  fat,  or  when  much  fat  is  mixed  thru  the  food  as  in  very 
rich  pastry.  The  retardation,  in  turn,  gives  an  opportunity  for  bac- 
terial action  in  the  interior  of  the  food  mass,  resulting  in  a  loss  of  food 
to  the  body  and  also  in  the  production  of  gases  and  even  of  poisonous 
substances.  This  is  the  explanation  of  much  of  the  indigestion  of 
which  people,  complain  after  eating  foods  rich  in  fat.  One  other  cause 
of  difficulty  in  the  digestion  of  fried  foods  is  that  the  fat  is  frequently 
overheated  during  cooking  and  is  thus  decomposed  into  substances  of 
an  irritating  character.  For  these  reasons,  pastry  and  fried  foods  do 
not  belong  in  the  child's  diet  nor  in  that  of  the  person  with  a  weak 
digestion.  Neither  should  they  be  eaten  frequently  nor  in  large 
amounts  by  anyone. 


'Langwortky  and  Holmes,  •'Digestibility  of  Some  Animal  Fats,"  U.S.  De- 
partment of  Agriculture,  Bulletin  310,  p.  21. 
H.  C.  Sherman,  "Food  Products,"  p.  389. 


19 1 7  | 


I' its  \m>  Oils  i\  Cooking 


Osborne  and  Mendel  and  also  McCollum  and  Davis1  have  been 
making  observations  on  the  influence  of  natural  fats  upon  growth. 
They  have  found  thai  butter  t'ai  is  valuable,  not  only  because  of  the 
fuel  value  which  it  has.  but  also  because  it  contains  certain  growth 
promoting  constituents,  not  found  in  all  fats.  Beef  fat  also  supplies 
these  substances,  but  in  a  smaller  amount.  Egg  yolk  fat  and  cod-liver 
oil,  too,  belong  in  this  list,  but  lard,  almond,  cottonseed,  and  olive 
oils,  altho  valuable  foods,  so  far  as  known  at  present  do  not  contain 
these  special  constituents.  It  is  evident,  then,  that  rich  milk,  cream, 
butter,  eggs,  fat  beef,  and  cod-liver  oil  arc  of  especial  value  in  growth 
and  also  in  eases  of  malnutrition. 

Fats  vary  in  their  cost.  Often  a  less  expensive  fat  answers  the 
purpose  as  well  as  a  more  expensive  one,  and  the  question  may  be 
worth  asking,  "'Are  we  paying  too  high  for  flavor?"  The  following 
table  shows  the  prices  (May,  1917)  for  some  common  fats. 

Table  2. — Prices  of  Some  Common  Fats 


Name  of  fat 


Olive  "il 

4  ounce  or  '  \    pint   bottle 

8   "inn ■  '.,    pint   can 

16  ounce  "i-  1  pint  can 

32   ounce  or  1   quart  can 

Butter , 

<  Heomargarine 

SCO 

Cottonseed  oil  l  Wesson  l 

Lard 

Hone1  rendered  lard    purchased  at  Is  cents 
|.rr  pound  exclusive  of  fuel) 

Home  rendered  lard  4-  gas 


I'i  ire  per  pound 


May,  1917 

$1.20 
.60 
.55 

.50 
.52 
.25 
.35 
.29 
.30 

.21 

99 


The  table  shows  not  only  the  range  in  prices,  but  also  the  advis- 
ability of  buying  oils  in  the  can  rather  than  in  bottles,  especially  when 
the  bottles  are  small  in  size.  The  can  is  of  additional  advantage,  as  it 
shuts  out  the  Light,  and  light  is  a  potent  factor  in  the  production  of 
rancidity.  The  differences  in  price  of  olive  oil  according  to  quantity 
purchased  are  illustrative  of  similar  differences  to  be  found  in  pur- 
chasing most  foods.  The  home  rendered  lard  may  be  more  or  less 
expensive  than  an  equally  good  grade  of  commercial  lard  according 
to  the  cost  of  fuel  and  the  value  of  the  housewife's  time. 


■Journal  of  Biological  Chemistry,  Vol.  XVI.  p.  123;  Vol.  XVII.  p.  401j  Vol. 
XX.  pp.  379,  'ill;   V<d.  XXI.  p.  17!»;   Vol.  XXIII.  p.  23]  ' 


8  University  of  Illinois  Bulletin  [July, 

The  initial  cost  of  a  fat  is  not  the  only  point  to  be  noted.  When 
used  for  shortening,  a  larger  amount  of  one  may  be  required  than  of 
another.  As  butter  is  only  85  percent  fat  while  lard,  oils,  and  Crisco 
are  100  percent,  less  of  these  is  required  than  of  butter.  Again,  in 
frying,  more  of  some  fats  is  absorbed  than  of  others.  In  cooking 
doughnuts,  different  fats  were  found  to  be  absorbed  according  to  the 
following  order:  olive  oil  (least),  Wesson  Oil,  Crisco,  lard,  lard  and 
suet  (most).  More  important  still,  from  the  standpoint  of  economy, 
is  the  question, ' '  Which  fat  can  be  used  the  greatest  number  of  times  f ' ' 
This  use  depends  primarily  upon  the  decomposition  temperatures.  In 
general,  such  fats  as  lard  or  lard  and  suet,  which  give  off  most  smoke 
at  frying  temperatures,  can  be  used  a  smaller  number  of  times  than 
can  those  giving  off  less  smoke,  as  Crisco  or  the  oils.  The  care  in  heat- 
ing and  the  method  of  clarifying  employed  by  the  housewife  also  help 
to  determine  the  number  of  times  the  fat  can  be  used.  Fat  once  over- 
heated until  it  smokes  excessively  can  never  be  used  as  long  as  can 
the  same  fat  not  so  overheated.  However,  Wesson  Oil  or  Crisco  do 
not  give  off  this  heavy  smoke  until  a  very  high  temperature  is  reached, 
but  lard  decomposes  so  rapidly  on  slight  overheating  that  much  care 
is  required  to  prevent  it. 

The  economy  of  substituting  less  expensive  fats  for  those  high 
priced  luxuries  can  easily  be  seen.  For  example,  one  cup  of  mayon- 
naise dressing  made  of  olive  oil  bought  by  the  quart  costs  27  cents, 
whereas  if  made  of  cottonseed  oil,  one  cup  costs  11.25  cents.  Again, 
the  substitution  of  one  cup  of  oleomargarine  for  one  cup  of  butter  in 
a  cake  gave  practically  identical  results  and  reduced  the  cost  by  8.5 
cents.  Partial  substitution  of  Crisco  might  profitably  have  reduced  it 
still  further.  In  some  cases,  fats  cannot  be  substituted  thus,  but  often 
the  question  of  substitution  becomes  merely  one  of  flavor  and  must  be 
determined  according  to  one's  taste  and  pocketbook. 

USES  IN  COOKERY 

Fats  are  used  in  cookery  for  three  general  purposes :  first,  to  flavor 
or  to  enrich  foods,  as  in  cooked  salad  dressing  and  white  sauce,  or  as 
an  emulsion  in  French  dressing  or  mayonnaise ;  second,  as  a  medium 
for  browning  and  cooking  in  sauteing  or  frying ;  and  third,  as  a  short- 
ening agent  in  flour  mixtures.  From  the  fats  available,  the  housewife 
must  select  one  which  imparts  an  agreeable  flavor  and  a  good  texture 
for  her  purpose. 


1917]  Fats  and  Oils  in  Cooki\-<;  9 

The  following  fats  were  tested  recently  in  cooking  experiments 
conducted  in  these  laboratories :  olive  oil,  Mazola,  Wesson  Oil,  chicken 
fat,  butter,  oleomargarine,  Snowdrift,  lard,  Crisco,  suet,  and  bacon 
drippings.  The  flavor  obtained  is  the  first  consideration.  Olive  oil 
gives,  in  all  cases  except  in  fried  foods,  a  very  pronounced  and  charac- 
teristic flavor.  This,  for  salad  dressing,  constitutes  its  chief  recommen- 
dation. Mazola,  a  corn  oil,  gives  a  flavor  only  a  little  less  strong,  but  it 
is  often  not  detected  unless  used  in  large  amounts.  Wesson  Oil  is  prac- 
tically tasteless.  Chicken  fat  has  its  own  distinctive  but  mild  flavor 
unless  tried  out  at  a  high  temperature ;  in  doughs  and  batters  its  use 
is  ordinarily  not  evident.  As  an  enriching  or  shortening  agent,  butter 
is  generally  used  and  directions  for  the  substitution  of  other  fats  are 
concerned  largely  with  methods  of  approximating  the  flavor  and 
texture  secured  with  butter.  Oleomargarine,  if  of  good  quality  and 
purchased  of  a  reliable  firm,  may  be  used  for  the  same  purposes  as  but- 
ter, in  all  sorts  of  cooking,  and  it  is  difficult  to  detect  even  in  mildly 
seasoned  sauces.  Snowdrift  is  a  very  white  fat  but  one  which  easily 
becomes  rancid.  In  these  tests  it  was  never  satisfactory  because  of 
the  strong,  disagreeable  flavor.  Lard  and  Crisco,  altho  differing  in 
source  and  smoking  points,  give  somewhat  similar  results  as  shortening 
agents.  Lard  can  almost  always  be  recognized  by  a  peculiar  charac- 
teristic sensation  in  the  mouth.  Crisco  gives  somewhat  the  same  sen- 
sation in  the  mouth  as  lard  but  to  a  lesser  degree.  It  ordinarily  has 
little  flavor,  altho  after  long  standing  it  may  become  strong.  Suet 
has  a  very  limited  use  because  it  can  practically  always  be  tasted  and 
its  hardness  gives  an  unpleasant  texture.  Bacon  drippings  are  strong 
flavored,  but  are  not  for  that  reason  necessarily  useless.  They  should, 
however,  be  restricted  to  sauteing  of  those  foods  in  which  the  added 
flavor  is  not  objectionable.  The  consistency  of  cooked  salad  dressings 
,and  of  mayonnaise,  the  color  secured  in  sauteing  or  deep-fat  frying, 
the  texture  of  muffins,  cakes,  and  pastry,  vary  somewhat  with  the  kind 
of  fat  used,  and  these  variations  will  be  discussed  later. 

COOKED  SALAD  DKESSING 

Recipes  for  cooked  salad  dressing  usually  call  for  butter  or  per- 
haps for  olive  oil,  but  cheaper  fats  may  be  substituted.  Wesson  Oil 
or  oleomargarine  can  easily  be  used,  but  the  taste  of  Mazola  is  imme- 
diately apparent  and  its  presence  must  depend  upon  whether  or  not 
one  likes  the  flavor  it  gives.  Crisco  and  lard  are  possible  altho  the 
discriminating  person  detects  them  easily.     Chicken  and  bacon  fats 


10  University  of  Illinois  Bulletin  [July, 

are  quite  noticeable,  but  may  be  a  desirable  addition  with  a  vegetable 
or  a  meat  salad.  Suet  is  disagreeable.  The  consistency  varies  so  little 
with  the  different  fats  as  to  be  quite  unimportant ;  so  the  selection  of 
the  fat  depends  upon  the  flavor  imparted.  In  other  words,  any  one  of 
several  common  fats  may  be  used  for  cooked  salad  dressings,  especially 
if  the  combination  is  carefully  considered.  If.  however,  cooked  salad 
dressing  is  made  in  large  quantities  and  used  from  time  to  time  for 
different  salads,  butter,  oleomargarine,  or  Wesson  Oil  is  best  because 
of  the  flavor. 

FRENCH  AND  MAYONNAISE  DRESSINGS 

For  French  dressing,  olive  oil  is  generally  recommended  but  Wes- 
son Oil  or  Mazola  may  be  used.  The  difference  between  a  dressing  made 
with  olive  oil  and  one  made  entirely  of  Wesson  Oil  is  the  absence  of 
the,  distinctive  olive  flavor  rather  than  any  added  taste.  Substituting 
Wesson  for  one-half  the  olive  oil  enables  one  to  secure  the  flavor  of  the 
more  expensive  product  and  at  the  same  time  to  lower  the  cost  consid- 
erably. The  presence  of  Mazola  is  very  evident  unless  the  dressing 
contains  at  least  one  part  of  vinegar  to  three  of  oil.  so  that  for  those 
who  do  not  like  a  very  tart  dressing,  Wesson  gives  the  best  results. 

For  mayonnaise  dressing,  Wesson  is  a  better  substitute  for  olive 
oil  than  Mazola,  for  the  flavor  of  Mazola  is  not  sufficiently  disguised 
by  the  smaller  proportion  of  other  ingredients.  Chicken  fat,  especially 
the  more  oily  portion,  can  be  utilized,  altho  the  flavor  is  evident.  If 
one  does  not  have  an  oil  at  hand,  mayonnaise  dressing  may  be  made 
with  washed  and  melted  butter,  oleomargarine,  or  melted  Crisco ;  half 
oil  and  half  washed  or  unsalted  butter  give  an  especially  well-flavored 
dressing  of  good  consistency. 

WHITE  SAUCE 

White  sauce  can  be  made  easily  with  fats  other  than  butter  if  the 
purpose  for  which  it  is  to  be  used  is  kept  in  mind.  For  example,  with 
finnan  haddie  the  flavor  of  the  partly  smoked  fish  is  so  pronounced  that 
almost  any  fat  can  be  used  in  the  sauce  without  being  detected ;  with 
creamed  meats,  the  use  of  drippings  is  sometimes  a  desirable  addition. 
Since  white  sauce  is  served  hot  and  the  proportion  of  fat  is  small,  no 
variation  in  consistency  is  apparent. 

SAUTEING 

In  sauteing,  a  golden  brown  color  and  a  good  flavor  are  the  desired 
ends.    The  color  usually  depends  upon  the  temperature  and  the  time 


191? \  Pats  and  Oils  in  Cooking  11 

of  cooking,  but  it  is  sometimes  heightened  by  the  discoloration  of  the 
fat.  Starch  and  sugar  brown  so  easily  that  flour  mixtures  or  meats 
rolled  in  bread  crumbs  acquire  a  good  color  whether  the  fat  contributes 
to  it  or  not,  but  some  vegetables  brown  with  such  difficulty  that  a  fat 
of  low  smoking  point,  as  suet  or  drippings,  gives  a  better  appearance. 
Altho  often  recommended,  butter  burns  so  easily  that,  when  it  is 
used,  il  is  difficult  to  avoid  a  very  uneven  color  and  often  an  unpleasant 
flavor.  Better  results  are  obtained  with  butter  as  well  as  with  suet 
and  drippings  if  some  other  fat  of  high  smoking  point,  like  Crisco  or 
"Wesson  Oil,  be  substituted  in  part.  Olive  oil  and  Mazola  give  charac- 
teristic flavors  which  may  or  may  not  be  liked.  Wesson  Oil  is  prac- 
tically tasteless,  and  consequently  can  be  very  generally  used.  More- 
over, because  of  its  high  smoking  point,  there  is  little  danger  of  scorch- 
ing. Chicken  fat,  bacon,  or  other  drippings  often  add  an  agreeable 
flavor  to  meats  or  vegetables,  but  they  must  be  selected  with  care  to 
avoid  unpleasant  combinations.  Lard  and  Crisco  are  so  nearly  taste- 
less that  like  Wesson  Oil  they  find  wide  use.  Suet,  because  of  its  flavor 
and  the  unpleasant  sensation  left  in  the  mouth  when  it  cools  even  a 
little,  is  better  used  in  small  quantities  or  with  other  fats. 

DEEP-FAT  FETING 

In  deep-fat  frying,  an  even  brown  color  and  a  pleasant  flavor,  with 
the  minimum  of  fat  absorption,  make  a  good  product.  The  color  de- 
pends upon  the  character  of  the  food  and  of  the  fat.  but  more  especially 
upon  the  temperature  and  the  time  of  cooking.  The  flavor  varies  with 
the  fat  used,  altho  the  differences  are  much  less  than  one  might 
expect.  For  example,  even  Mazola  and  chicken  fat  give  little  taste 
to  doughnuts  and  none  at  all  to  French  fried  potatoes  sprinkled 
with  salt.  While  strongly  flavored  fats  need  not  always  be  discarded, 
those  with  little  flavor  are  safest  for  general  use.  The  smoking  point 
of  fats  also  determines  the  quality  of  the  finished  product,  for  when 
fats  smoke,  decomposition  is  taking  place  at  a  rather  rapid  rate,  pro- 
ducing an  unpleasant  flavor.  Moreover,  fats  which  have  become  dis- 
colored by  decomposition  do  not  produce  as  even  a  color  in  frying. 
Consequently,  lard  which  is  used  "smoking  hot"  is  less  satisfactory 
than  Crisco,  Mazola,  or  Wesson  Oil,  which  give  no  smoke  at  any  ordi- 
nary cooking  temperature.  (See  Table  1,  page  4.)  The  high  smoking 
point  of  chicken  fat  makes  it  especially  desirable  for  frying,  but  it  is 
not  often  obtained  in  the  ordinary  home  in  quantity  sufficient  for  that 
purpose.  Moreover,  chicken  fat  is  very  much  the  best  butter  substi- 
tute for  shortening  and  should  be  reserved  for  that  purpose. 


12  University  op  Illinois  Bulletin  [July, 

Greasiness  is  somewhat  dependent  upon  the  kind  of  fat  nsed  but 
much  more  dependent  upon  the  food  to  be  cooked  and  the  temperature 
employed.  Rich  doughs  and  batters  become  more  grease  soaked  in  fry- 
ing than  those  containing  less  shortening,  and  foods  cooked  at  too  low 
a  temperature  absorb  a  large  amount  of  fat  because  the  protecting 
coating  is  formed  less  quickly  than  at  a  higher  temperature  and  because 
the  material  stays  in  the  fat  for  a  longer  time.  Doughnuts  made  with- 
out shortening  absorb  much  less  fat  than  those  in  which  shortening  is 
used.  Because  at  least  a  small  amount  of  fat  is  taken  up  in  frying,  a 
fat  with  little  flavor  and  a  high  smoking  point  is  best  for  general  use. 
Of  the  fats  used,  Wesson  Oil  and  Crisco  fulfil  the  conditions  best. 

SHORTENING 

DOUGHS  AND  BATTERS 

With  doughs  and  batters,  the  kind  of  fat  to  be  used  varies  with  the 
amount  required,  for  with  the  possible  exception  of  butter,  no  one  fat 
gives  a  uniformly  good  texture  and  flavor  in  all  mixtures.  Since  dif- 
ferences produced  in  texture  are  neither  marked  nor  important  except 
in  cakes  and  rich  muffins,  the  choice  in  mixtures  containing  little  fat 
is  governed  by  flavor.  In  griddle  cakes,  any  fat  except  olive  oil  can 
be  used,  but  the  griddle  should  be  greased  with  one  having  little  flavor. 
For  muffins,  butter  gives  the  best  flavor  and  the  greatest  tenderness, 
but  oleomargarine  or  chicken  fat  produces  an  almost  identical  product. 
Crisco,  lard,  or  Wesson  Oil  gives  good  results  provided  a  little  extra 
salt  is  added ;  of  the  three,  lard  is  the  most  easily  detected.  Mazola  is 
too  apparent  to  be  desirable,  and  drippings  and  suet  are  so  strongly 
flavored  as  to  be  impossible.  For  biscuits,  the  same  fats  may  be  used 
as  for  muffins  except  that  the  failure  to  increase  the  salt  is  more  serious 
and  that  Crisco  seems  to  produce  a  somewhat  coarser  texture.  For  the 
richer  shortcake  mixture,  a  fat  with  little  flavor,  like  Crisco,  lard,  or 
Wesson  Oil,  is  best  with  the  exception  of  chicken  fat.  For  both  bis- 
cuit and  shortcake,  to  secure  the  best  texture,  oils  when  used  should 
be  mixed  with  the  liquid  rather  than  with  the  flour. 

CAKES 

With  the  exception  of  pastry,  cake  is  the  richest  mixture  used. 
For  that  reason,  care  is  needed  in  the  selection  of  the  fat,  but  since  the 
flavor  is  often  disguised  by  extracts,  spices,  or  chocolate,  a  compara- 
tively large  number  of  fats  are  possible. 


1917]  Fats  and  Oils  in  Cooking  n 

One  of  the  characteristics  of  a  good  cake  is  tenderness.  The 
influence  of  the  mixing  upon  tenderness  is  well  known,  but  varia- 
tions due  to  the  kind  of  fat  used  are  often  not  sufficiently  empha- 
sized. The  most  tender  cake  is  obtained  with  butter.  This  does  not 
mean  that  a  good  cake  cannot  be  made  with  other  fats  but  merely 
that  if  two  cakes  are  made  from  the  same  recipe  and  with  the  same 
method  of  mixing,  one  with  butter  and  the  second  with  some  other 
fat,  the  one  in  which  butter  has  been  used  seems  the  more  tender. 
The  nearest  approach  to  the  texture  of  a  butter  cake  is  obtained  with 
chicken  fat  or  oleomargarine.  Contrary  to  what  one  might  expect  from 
the  results  with  chicken  fat,  oils  do  not  produce  good  cake.  The  cake 
seems  dry  and  breadlike,  while  if  more  fat  is  added,  it  becomes  greasy, 
and  if  more  liquid,  coarse.  Since  butter  is  85  percent  fat  and  lard  and 
Crisco,  100  percent,  in  substituting  either  for  butter,  to  secure  the  same 
richness,  the  quantity  should  be  reduced  about  one-eighth.  Increasing 
the  liquid  slightly  to  allow  for  the  moisture  of  the  butter  improves  the 
texture.  The  amount  of  beating  is,  however,  the  most  important 
factor,  for  beating  increases  the  tenderness  and  the  apparent  richness 
of  any  cake.  A  butter  cake  made  with  the  minimum  of  beating  may  be 
tender,  but  one  with  Crisco  is  dry  and  lacking  in  richness  if  beaten  too 
little.  To  secure  the  best  possible  texture  in  substituting  Crisco  or 
lard  for  butter,  the  amount  of  fat  should  be  decreased  one-eighth,  the 
liquid  should  be  slightly  increased,  and  care  should  be  taken  to  beat 
the  cake  well. 

Butter  gives  not  only  the  best  texture  but  the  best  flavor  also,  and 
if  it  is  used  at  all  in  baking,  it  should  be  for  cake.  The  best  substitute, 
from  the  standpoint  both  of  flavor  and  texture,  is  oleomargarine  or 
chicken  fat  with  increased  salt,  and,  as  has  been  said  before,  the  best 
use  for  the  limited  amount  of  chicken  fat  usually  obtained  in  the  home, 
is  as  a  butter  substitute  in  cakes.  For  a  white  cake,  where  it  is  desired 
to  avoid  all  color,  Crisco  is  the  best  shortening  agent,  if  the  precau- 
tions noted  in  the  discussion  of  texture  in  cakes  are  observed.  Lard 
tho  often  used,  is  more  easily  detected  than  Crisco  and  hence  is  less 
satisfactory.  It  can,  however,  be  used  safely  with  spices  or  any  strong 
flavoring  extract.  Snowdrift,  altho  very  white,  is  very  apparent  and 
unpleasant  in  flavor  even  in  spice  cake.  The  oils  are  not  desirable 
because  of  the  texture  produced. 


14 


University  of  Illinois  Bulletin 


[July, 


PASTRY 

For  plain  pie  crust,  lard  gives  the  tenderest  and  flakiest  product. 
A  good  crust  can  be  secured  with  oils  if  they  are  properly  handled  but 
a  mealy  rather  than  a  flaky  texture  is  the  result.  Not  more  than  one 
part  of  oil  to  four  of  flour  should  be  used,  and  care  should  be  taken  to 
mix  the  oil  and  flour  only  slightly.  Otherwise  so  little  water  can  be 
added  that  the  pie  crust  is  very  difficult  to  handle  and  crumbles  to 
pieces  when  baked.  Chicken  fat  gives  a  good  crust  but  it  should  be 
handled  like  the  oils.  Butter  produces  a  crust  of  delicious  flavor  for 
those  who  are  willing  to  pay  the  price,  but  the  texture  is  no  better 
than  with  lard  and  often  not  so  good.  Sour  cream  when  used  in  some- 
what larger  proportion  than  the  oils  requires  a  little  soda  to  neutralize 
the  acid,  but  gives  a  very  good  quality  of  crust  and  one  tasting  much 
like  a  butter  crust.  No  water  can  be  used,  as  there  is  sufficient  liquid 
in  the  cream.  Oleomargarine  gives  a  crust  almost  impossible  to  detect 
from  one  made  with  butter.  A  crust  made  with  Crisco  closely  resem- 
bles one  made  with  lard.  Suet  does  not  give  a  good  texture  and  both 
suet  and  drippings  are  too  strongly  flavored  to  be  desirable. 

SUMMARY 

The  problem  of  the  housewife  in  the  use  of  fats  and  oils  in  cookery 
is  largely  one  of  understanding  the  possibilities  and  limitations  of  her 
particular  supply,  and  of  using  that  supply  as  economically  as  possible. 
This  involves  an  understanding  of  the  possible  substitutions  of  one 
fat  for  another,  with  some  knowledge  of  their  comparative  costs.  The 
following  table  shows  the  possible  uses  of  the  ordinary  fats. 


Table  3. — Summary  of  Uses  of  Easily  Obtainable  Fats 


Kinds  of  fat 

Flavor 

Uses 

Olive  oil 

Strong 
Slight 

Fairly  strong 

Mild 

Mild 

Mild 

Often  strong 
Slight 

Strong 
Very  strong 
Mild 

Uncooked  salad  dressings 
Deep-fat   frying,  salad   dressings, 

shortening  except  cakes 
Deep-fat  frying 
Shortening,  especially  cakes 
Shortening,  except  of  plain  pastry 
Shortening,    especially     of     plain 

pastry 
Frequently  too  strong  for  use 
Sauteing,  deep-fat  frying,  short- 
ening 
.  Sauteing 

Wesson  Oil 

Mazola 

Butter 

Snowdrift 

Suet 

Bacon  fat 

Sauteing 
Same  as  butter 

Oleomargarine 

1917]  Cooking  Temperate  15 

COOKING  TEMPERATURES 

USES  OF  THE  THERMOMETER 

No  factor  in  the  preparation  of  food  so  largely  determines  the 
results  as  does  heat.  Upon  it s  proper  application  depends  the  texture 
and  finality  of  a  produd  and  also  the  development  of  the  finer  flavors. 

Exact  results  can  he  obtained  only  by  the  use  of  accurate  methods. 
and  the  thermometer  furnishes  the  only  really  accurate  method  of 
determining  the  degree  of  heat  thai  is  being  applied.     Satisfactory 

results  may  be  produced  by  the  use  of  good  judgment  only,  but 
good  judgment  requires  repeated  observation,  training,  and  skill,  is 
acquired  slowly,  and  is  dependable  only  after  years  of  experience. 
Judgment,  developed  by  experience,  enables  one  to  tell  the  time  of 
day  by  the  sun.  hut  a  watch  is  much  more  easily  used  and  is  a  more 
accurate  gage. 

Housewives  employ  many  little  devices  which  show  their  need  of 
a  definite  measure  for  temperature.  Thus  a  bit  of  flour  or  bread  is 
browned  in  the  oven,  a  small  preliminary  cake  is  baked,  or  a  piece  of 
bread  is  browned  in  hot  fat  in  "  forty  counts''  before  frying  croquettes 
or  in  "sixty  counts"  before  frying  doughnuts.  The  woman  who  uses 
gas  learns  to  light  the  burner  a  definite  time  before  putting  her  bread 
to  hake,  and  then  turns  the  flame  off  onedialf  or  one-third.  All  of 
these  devices  show  an  attempt  to  obtain  exact  methods  of  applying 
heat. 

The  chemical  thermometers  give  very  accurate  results.  They  do. 
however,  have  the  serious  drawback  of  being  easily  broken  and  of  re- 
quiring a  hole  in  the  top  or  side  of  the  oven  for  their  insertion.  The 
mercury  bulb  should  he  as  near  as  possible  to  the  food  being  cooked, 
since  the  temperature  at  tin1  top  or  at  the  side  of  the  oven  is  not  the 
same  as  in  the  center.  If  the  thermometer  is  inserted  thru  the  side, 
just  below  the  grate,  the  bulb  is  then  immediately  below  the  food  being 
cooked.  These  chemical  thermometers  can  he  had  ranging  from  the 
six-inch  KM)  < '.  thermometers,  which  may  be  inserted  in  a  roast,  up 
to  those  registering  300  < '.  and  recording  as  high  temperatures  as  are 
ever  used   in  cookery. 

Thermometers  on  stands,  which  may  be  placed  beside  the  bread 
or  cake  in  the  oven  and  which  are  less  easily  broken,  may  also  be  had 
in  the  Fahrenheit  scale.  These  are  sufficiently  sensitive  for  ordinary 
purposes,  as  they  record  the  temperature  to  within  ten  degrees  of  the 
chemical  thermometer.  They  are  especially  satisfactory  when  used  with 
an  oven  having  a  <rlass  door.     When  used  in  a  coal  range  and  placed 


16  University  of  Illinois  Bulletin  [July, 

directly  on  the  bottom  of  the  oven,  a  temperature  of  approximately 
85°  F.  lower  than  the  required  gas  oven  temperature  should  be  used 
because  of  the  difference  in  the  course  of  the  heat  in  the  two  stoves. 

Stove  manufacturers  are  recognizing  the  value  of  a  heat  gage 
and  are  putting  thermometers  on  the  outside  of  their  ovens.  Such 
thermometers  are  of  considerable  value  and  aid  greatly  in  determining 
the  temperature.  Heretofore  we  have  sought,  in  our  laboratories,  to 
record  chiefly  the  temperature  in  the  center  of  the  oven,  and  have  not 
relied  to  any  extent  upon  thermometers  which  register  the  heat  else- 
where. Since  these  thermometers  on  the  outside  seem  to  be  most 
practicable  and  most  easily  observed,  we  may,  with  profit,  learn  to  use 
a  slightly  different  set  of  temperatures- based  on  their  records.  Start- 
ing with  those  temperatures  taken  at  the  center  of  the  oven,  we  must 
make  allowance  for  the  fact  that  the  outside  thermometer  will  record 
the  heat  more  slowly,  and  will  register  a  temperature  of  about  50°  F. 
lower  than  the  thermometer  in  the  center. 

The  table  on  the  opposite  page  shows  the  range  of  temperatures 
applicable  in  the  preparation  of  foods,  as  worked  out  in  these  labora- 
tories. 

DISCUSSION  OF  TEMPERATURE  TABLE 

Water  is  frozen  at  0°  C,  but  fruit  ices  or  ice  creams  freeze  at  a 
lower  temperature.  Substances  in  solution  lower  the  freezing  point, 
and  the  more  concentrated  the  solution,  the  lower  the  temperature  re- 
quired to  freeze  it.  Thus,  a  mixture  may  be  prepared  containing  so 
much  pulp  and  sugar  that  it  is  almost  impossible,  by  ordinary  methods, 
to  freeze  it.  Under  such  circumstances,  the  remedy  lies  in  diluting  the 
mixture  and  adding  more  salt  to  the  crushed  ice.  Three  parts  of  ice 
to  one  part  of  salt  ordinarily  gives  a  sufficiently  low  temperature  for 
freezing  ices  and  ice  creams,  but  adding  more  salt  produces  a  still 
lower  temperature. 

Water  simmers  before  it  boils.  Tiny  bubbles  rise  and  break  under 
the  surface  of  the  water,  and  some  form  about  the  edges  of  the  pan. 
When  water  boils,  however,  the  surface  is  completely  agitated.  Above 
sea  level,  the  boiling  point  may  be  reached  at  98°  C.  or  99°  C.  or  lower, 
according  to  the  altitude.  Simmering  temperature  is  used  in  the  cook- 
ing of  meat  stews  and  of  so  called  "boiled"  meats. 

The  boiling  point  of  a  sugar  solution  is  higher  than  that  of  water, 
as  substances  in  solution  raise  the  boiling  point.  The  temperatures 
given  in  the  preceding  table  should  be  lowered  1°  C.  for  every  degree 
below  100°  C.  found  as  the  boiling  point  of  water.  If  the  boiling  point 
is  99°  C,  then  fondant  frosting  is  best  at  112°  C,  etc.    Most  satisfac- 


1917] 


Cooking  Temperatures 
Table  of  Temperatures 


17 


Process 


Degrees 

Degrees 

Centigrade 

Fahrenheit 

-5  to  -8 

23  to  18 

0 

32 

3  to  10 

37  to  50 

15  to  16 

60 

26  to  40 

79  to  104 

37  to  60 

98.6  to  140 

(Depends  upon  acidity) 

Begins  56;  completes  71 

133  to  160 

82  to  99 

180  to  210 

82  to  84 

179  to  183 

89  to  94 

192  to  201 

100 

212 

103 

185 

113 

235 

111 

232 

113  to  115 

235  to  239 

117 

243 

125 

257 

122 

252 

250 

450 

175 

347 

46.5  to  60 

115.7  to  140 

60  to  70 

140  to  158 

70  to  80 

158  to  176 

175  to  190 

347  to  374 

185  to  205 

365  to  401 

190  to  195 

374  to  383 

175  to  190 

347  to  374 

150  to  170 

302  to  338 

200 

392 

180  to  220 

356  to  428 

190 

374 

210 

410 

220  to  235 

428  to  455 

235 

455 

235 

455 

235  to  240 

455  to  464 

235  to  200 

455  to  392 

240 

464 

Freezing  of  fruit  ices   (temperature  of 

medium)    

Freezing  of  water 

Whipping  of  cream 

Batter-making 

Raising  of  bread  (temperature  of  room) 
Cheese-making 

Coagulation  of  albumin 

Simmering  of  water 

Soft   custards    

Double  boiler,  top  part 

Boiling  water  at  sea  level 

Jellies  (boiling  point  of  water  100°  C.) 
Sugar  cookery  (boiling  point  of  water 
100°  C.) 

Fondant  

Fudge  frosting,  boiled 

1  egg  white  to  1  cup  sugar 

2  egg  whites  to  1  cup  sugar... . 
1  egg  white  to  1  cup  of  dark 

brown  sugar 

1  egg  white  to  %  cup  of  dark 
brown  sugar,  %  cup  white 
'Roasting  of  meat 

Temperature  of  oven 

First  15  minutes 

Remainder  of  time 

Temperature  of  meat  interior 

Rare  done  

Medium   

Well  done   

Deep-fat  frying.  Temperature  of  fat  for 

Uncooked  foods   

Cooked  foods  

Cold,  wet,  uncooked  foods 

Baking.    Temperature  of  center  of  oven 
for 

Sponge  cakes  

Angel  food  cakes 

Souffles  (surrounded  by  water) .... 

Bread 

Butter  cakes 

Loaf   

Layer  

Muffins  . 

Parkerhouse  rolls   

Baked  potatoes   

Baking  powder  biscuit 

Popovers  

'Pastry    


"Elizabeth  Sprague  and  H.  C.  Grindley,  "A  Precise  Method  of  Roasting 
Beef,"  University  of  Illinois  Bulletin,  Vol.  IV,  No.  19. 

'Elizabeth  Sprague,  "Studies  of  Methods  in  Food  Preparation,"  Journal  of 
Home  Economics,  Vol.  Ill,  No.  5,  p.  446. 


/ 


UNIVERSITY  OF  ILLINOIS-URBANA 


18  University  of  Illinois  Bu  3  0112  096200461 

tory  results  have  been  obtained  in  sugar  cookery  on  rainy  days  by  first 
taking  the  temperature  of  boiling  water  and  then  raising  the  tempera- 
ture for  the  cooking  of  the  sugar  solution  to  accord.  The  lower  tem- 
peratures given  produce  a  softer  frosting  which  requires  more  beating 
and  hardens  more  slowly.  The  addition  of  egg  white  to  a  frosting  or 
a  candy  will,  it  may  be  noted,  raise  the  required  temperature  for  the 
syrup.  The  larger  amount  of  egg  is  often  desirable  as  it  makes  a  frost- 
ing which  spreads  easily  and  which  keeps  soft  on  the  inside.  The  pres- 
ence of  caramel  raises  the  temperature  to  which  sugar  solutions  should 
be  cooked.  Thus  the  soft  ball  test  for  dark  brown  sugar,  which  con- 
tains a  considerable  amount  of  caramel,  is  119°  C.  instead  of  113°  C, 
as  for  white  sugar.  This  applies  in  the  making  of  boiled  frostings, 
when  dark  brown  sugar  is  used.  The  temperature  required  rises  in 
accordance  with  the  proportion  of  this  sugar  substituted. 

Cream  whips  best  at  5°  C,  especially  if  it  is  not  very  thick.  If 
the  temperature  is  as  high  as  15°  C.  or  16°  C,  the  butter-making  point 
is  reached  and  a  little  overheating  gives  a  granular  appearance  and 
continued  beating  may  produce  butter.  The  proper  temperature  in 
the  making  of  butter  causes  it  to  form  much  more  readily  and  to  give 
a  larger  bulk  with  a  better  color  and  consistency. 

The  best  quality  of  cottage  cheese  is  made  when  the  curd  is  sepa- 
rated from  the  whey  by  means  of  the  sun's  heat  or  at  a  temperature  of 
37°  C,  in  a  double  boiler.  However,  the  milk  must  be  fairly  acid  to  sep- 
arate at  this  temperature ;  otherwise,  it  may  be  necessary  to  use  a  higher 
one.  In  any  case,  a  double  boiler  should  be  used,  and  the  temperature 
never  allowed  to  go  much  above  70°  C,  as  the  curd  will  then  toughen. 

Since  eggs  contain  much  albumin,  the  egg  can  be  completely  coagu- 
lated, even  made  firm,  at  a  temperature  of  71°  C.  or  72°  C.  At  this 
temperature,  the  egg  white  is  not  made  tough  and  rubbery  as  at  higher 
temperatures.  Hard  cooked  eggs  are  much  more  tender  if  cooked  for 
forty-five  minutes  at  75°  C.  than  if  boiled  for  ten  minutes.  Likewise, 
soft  cooked  eggs  are  much  better  if  cooked  for  five  to  ten  minutes  at 
about  75°  C,  than  if  boiled  for  three  minutes.  Approximately  this 
temperature  is  obtained  when  eggs  are  put  into  boiling  water  and 
allowed  to  stand,  with  the  heat  turned  off. 

Soft  custards  are  thickened  by  means  of  egg  and,  on  overcooking, 
curdle  because  the  protein  of  the  egg  toughens  and  shrinks.  The 
changes  take  place  very  rapidly,  so  that  much  care  is  required  in  the 
testing.  The  presence  of  egg  white  lowers  the  curdling  point ;  thus  a 
custard  made  from  egg  whites  curdles  at  83°  C,  one  made  from  whole 
egg  at  83.5°  C,  and  one  made  from  yolks  at  84.5°  C.     The  optimum 


UNIVERSITY  OF  ILLINOIS-URBANA 


12  096869620 


•■;:■■'   ':,-l;v.,   :; 

IhhRbk 


